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Dear Gap Forum,

Vahid Dabbaghian asked

I want to get the character tables of the central extensions of group

PSL(3,4) but I don't know how I can define these extensions.

If only the character tables are needed and not the groups themselves

then most of this information is available in the GAP character table

library.

The tables of the maximally cyclic central extensions are available

as `CharacterTable( "12_1.L3(4)" )' and `CharacterTable( "12_2.L3(4)" )',

and the table of the extension by a central group $2^2 \times 3$ is

available as `CharacterTable( "(2^2x3).L3(4)" )';

the ordering of classes and characters in these tables is compatible

with that in the ATLAS of Finite Groups.

The table of the Schur cover, which has the structure

$(4^2 \times 3).L_3(4)$, is currently not available in the GAP character

table library, but it would not be difficult to compute it from the

tables of the cyclic central extensions.

Kind regards,

Thomas

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